Algebra
If a ball and a bat together cost $1.10, and the bat costs $1.00 more than the ball, how much does the ball cost?
$0.05
For what value of x does 1 + x + x^2 + x^3 … = 4?
3/4
How many people are in this room right now? Include teachers, anyone asking questions, etc., as of the moment this question appeared on the screen.
lemme count
How many people must be in a room together for there to be a 50% chance that at least 2 of them share a birthday?
23
I have three happy little integers: 2, 3, and 6! What is the value of their least common multiple?
720
There is exactly one quadratic of the form ax^2 + bx + c (where a, b, and c are relatively prime) that passes through the points (-1, 2), (-2, 3), and (3, 8). What is a+b-c?
-1
What is the units digit of 13^2023?
7
Nebraska, the home of the AMC, changed its license plate scheme. Each old license plate consisted of a letter followed by four digits. Each new license plate consists of three letters followed by three digits. By how many times is the number of possible license plates increased? (exponents and fractions in your answer, like (2^2)/5, are fine)
26^2/10
Name three math concepts named for (not necessarily by) Euler.
Valid answers include: number, formula, identity, method, function, constant, method, transform, characteristic (E-V+F), etc.
Use operations on 8 8 8 to = 6. For example (9+9)/√(9) = 6. In this problem, roots higher than two are not operations.
hope you're right >:)
A palindrome, such as 83438, is a number that remains the same when its digits are reversed. The numbers x and x+32 are three-digit and four-digit palindromes, respectively. What is the sum of the digits of x?
24
The product (8) * (888...8), where the second factor has k digits, is an integer whose digits have a sum of 1000. What is k?
991
Dylan has a 100×100 square, and wants to cut it into pieces of area at least 1. Each cut must be a straight line (not a line segment) and must intersect the interior of the square. What is the largest number of cuts he can make?
9999
Who is Mr. Barnes' favorite artist? (hope you know this one by now)
Bruce Springsteen
David has an infinite supply of 4 dollar bills and Jennifer has an infinite supply of 5 dollar bills in Barnes Bank. If David and Jennifer withdrew some amount of money, what is the largest amount they could not have combined?
$11
Find c if a, b, and c are positive integers which satisfy c=(a+bi)^3 - 107i, where i^2 = -1
c = 198 :)
The first four terms in an arithmetic sequence are x+ y, x−y, xy, and x/y, in that order. What is the fifth term?
123/40
Select numbers a and b between 0 and 1 independently and at random, and let c be their sum. Let A, B and C be the results when a, b and c, respectively, are rounded to the nearest integer. What is the probability that A + B= C?
¾
Of its 64 recipients, how many women have won the Fields medal?
Two
What is k in the following sequence? (Jeffrey stole this problem from UIL--blame him, not me)
3 4 7 10 16 21 30 40 k 82 118
57
If a ≥ b > 1, what is the largest possible value of log_a(a/b) + log_b(b/a)?
[HINT: Use the AM-GM inequality]
0
Compute the largest prime factor of 3(3(3(3(3(3(3(3(3(3(3+1)+1)+1)+1)+1)+1)+1)+1)+1)+1)+1
73
You are walking up an infinitely long set of stairs. You can either take 2 steps or 1 step at a time (but not 3 or more). How many ways can you climb to the 8th step?
34
Name both of Ms. Chen's children. Then, suggest a name for her third child based off of this pattern.
Jacob, Aaron (sp?)
There's a famous AMC problem that goes here, but I think I've forgotten it. Anyway, what day of the week was Dickens born?
Friday